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Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…

This paper studies the estimation of large precision matrices and Cholesky factors obtained by observing a Gaussian process at many locations. Under general assumptions on the precision and the observations, we show that the sample…

This paper presents a new modeling strategy for joint unsupervised analysis of multiple high-throughput biological studies. As in Multi-study Factor Analysis, our goals are to identify both common factors shared across studies and…

We propose a fast and flexible method to scale multivariate return volatility predictions up to high-dimensions using a dynamic risk factor model. Our approach increases parsimony via time-varying sparsity on factor loadings and is able to…

Dimension reduction algorithms aim to discover latent variables which describe underlying structures in high-dimensional data. Methods such as factor analysis and principal component analysis have the downside of not offering much…

Deep Learning and factorization-based collaborative filtering recommendation models have undoubtedly dominated the scene of recommender systems in recent years. However, despite their outstanding performance, these methods require a…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

The model implied by factor score predictors does not reproduce the non-diagonal elements of the observed covariance matrix as well as the factor loadings. It is therefore investigated whether it is possible to estimate factor loadings for…

This paper introduces a novel sparse latent factor modeling framework using sparse asymptotic Principal Component Analysis (APCA) to analyze the co-movements of high-dimensional panel data over time. Unlike existing methods based on sparse…

Two key challenges in modern statistical applications are the large amount of information recorded per individual, and that such data are often not collected all at once but in batches. These batch effects can be complex, causing…

Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…

This article focuses on inference in logistic regression for high-dimensional binary outcomes. A popular approach induces dependence across the outcomes by including latent factors in the linear predictor. Bayesian approaches are useful for…

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

Recently, considerable interest has focused on variable selection methods in regression situations where the number of predictors, $p$, is large relative to the number of observations, $n$. Two commonly applied variable selection approaches…

This paper develops an inferential theory for high-dimensional matrix-variate factor models with missing observations. We propose an easy-to-use all-purpose method that involves two straightforward steps. First, we perform principal…

Extracting governing equations from dynamic data is an essential task in model selection and parameter estimation. The form of the governing equation is rarely known a priori; however, based on the sparsity-of-effect principle one may…

We develop a factor analysis for mixed continuous and binary observed variables. To this end, we utilized a recently developed multivariate probability distribution for mixed-type random variables, the Gaussian-Grassmann distribution. In…

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…

Factor models are widely used for dimension reduction. Bayesian approaches to these models often place a prior on the factor loadings that allows for infinitely many factors, with loadings increasingly shrunk toward zero as the column index…